A framework is provided for scaling and scale issues in hydrology. The first section gives some basic definitions. This is important as researchers do not seem to have agreed on the meaning of concepts such as scale or upscaling. ‘Process scale’, ‘observation scale’ and ‘modelling (working) scale’ require different definitions. The second section discusses heterogeneity and variability in catchments and touches on the implications of randomness and organization for scaling. The third section addresses the linkages across scales from a modelling point of view. It is argued that upscaling typically consists of two steps: distributing and aggregating. Conversely, downscaling involves disaggregation and singling out. Different approaches are discussed for linking state variables, parameters, inputs and conceptualizations across scales. This section also deals with distributed parameter models, which are one way of linking conceptualizations across scales. The fourth section addresses the linkages across scales from a more holistic perspective dealing with dimensional analysis and similarity concepts. The main difference to the modelling point of view is that dimensional analysis and similarity concepts deal with complex processes in a much simpler fashion. Examples of dimensional analysis, similarity analysis and functional normalization in catchment hydrology are given. This section also briefly discusses fractals, which are a popular tool for quantifying variability across scales. The fifth section focuses on one particular aspect of this holistic view, discussing stream network analysis. The paper concludes with identifying key issues and gives some directions for future research.

/pdf/scale-issues-in-hydrological-modelling-a-review-1x61lpwqjr.pdf

Scale issues in hydrological modelling: A review

Hydrology does not yet possess a generally agreed upon catchment classification system. Such a classification framework should provide a mapping of landscape form and hydro-climatic conditions on catchment function (including partition, storage, and release of water), while explicitly accounting for uncertainty and for variability at multiple temporal and spatial scales. This framework would provide an organizing principle, create a common language, guide modeling and measurement efforts, and provide constraints on predictions in ungauged basins, as well as on estimates of environmental change impacts. In this article, we (i) review existing approaches to define hydrologic similarity and to catchment classification; (ii) discuss outstanding components or characteristics that should be included in a classification scheme; and (iii) provide a basic framework for catchment classification as a starting point for further analysis. Possible metrics to describe form, hydro-climate, and function are suggested and discussed. We close the discussion with a list of requirements for the classification framework and open questions that require addressing in order to fully implement it. Open questions include: How can we best represent characteristics of form and hydro-climatic conditions? How does this representation change with spatial and temporal scale? What functions (partition, storage, and release) are relevant at what spatial and temporal scale? At what scale do internal structure and heterogeneity become important and need to be considered?

/pdf/catchment-classification-and-hydrologic-similarity-56ldm48oha.pdf

Catchment Classification and Hydrologic Similarity

[1] This study explores various aspects of catchment hydrology based on a mechanistic modeling of distributed watershed processes. A new physics-based, distributed-parameter hydrological model that uses an irregular spatial discretization is introduced. The model accounts, on a continuous basis, for the processes of rainfall interception, evapotranspiration, moisture dynamics in the unsaturated and saturated zones, and runoff routing. Simulations of several mid- to large-sized watersheds (∼103 km2) highlight various dynamic relationships between the vadose zone–groundwater processes and their dependence on the land surface characteristics. It is argued that the model inferences can be used for interpretation of distributed relationships in a catchment. By exploiting a multiple-resolution representation, the hydrologic features of the watershed terrain are captured with only 5–10% of the original grid nodes. This computational efficiency suggests the feasibility of the operational use of fully distributed, physics-based models for large watersheds.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004WR003218

Catchment hydrologic response with a fully distributed triangulated irregular network model

[1] A series of numerical experiments was carried out to test the hypothesis that temporal variability of rainfall intensity during a storm can cause the commonly observed decrease in runoff coefficients with increasing slope length. The results demonstrate significant effects over even relatively short slope lengths. Sensitivity analyses show that the scale dependency of measured runoff coefficients is most sensitive to the infiltration parameters of the slope. Furthermore, it is also sensitive to the slope angle and the friction factor of the surface, because these parameters control the depth of overland flow. These results suggest that the combination of time-varying rainfall intensity during an event and run-on infiltration can provide an alternative to spatial variation in infiltration as an explanation for the scale-dependency of runoff coefficients that has been observed in the field. Overland-flow models which simply use the mean rainfall intensity are also shown to underpredict the runoff quite dramatically. The results imply that a better understanding of the temporal variability of rainfall intensities is important in both understanding field measurements and developing robust models of overland flow.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000WR000188

The effect of temporal variations in rainfall on scale dependency in runoff coefficients

. Hydrologic response in natural catchments is controlled by a set of complex interactions between storm properties, basin characteristics and antecedent wetness conditions. This study investigates the transient runoff response to spatially-uniform storms of varying properties using a distributed model of the coupled surface-subsurface system, which treats heterogeneities in topography, soils and vegetation. We demonstrate the control that the partitioning into multiple runoff mechanisms (infiltration-excess, saturation-excess, perched return flow and groundwater exfiltration) has on nonlinearities in the rainfall-runoff transformation and its scale-dependence. Antecedent wetness imposed through a distributed water table position is varied to illustrate its effect on runoff generation. Results indicate that transitions observed in basin flood response and its nonlinear and scale-dependent behavior can be explained by shifts in the surface-subsurface partitioning. An analysis of the spatial organization of runoff production also shows that multiple mechanisms have specific catchment niches and can occur simultaneously in the basin. In addition, catchment scale plays an important role in the distribution of runoff production as basin characteristics (soils, vegetation, topography and initial wetness) are varied with basin area. For example, we illustrate how storm characteristics and antecedent wetness play an important role in the scaling properties of the catchment runoff ratio.

https://hal.archives-ouvertes.fr/hal-00305103/document

Controls on runoff generation and scale-dependence in a distributed hydrologic model

This paper focuses on the problem of quantifying real world catchment response using a distributed model and discusses the ability of the model to capture that response. The rainfall–runoff responses of seven small agricultural catchments in the eastern wheatbelt region of south-western Australia are examined. The variability in runoff generation and the factors that contribute to that variability (i.e. rainfall intensity, soil properties and topography) are investigated to determine if their influence can be captured in a mathematical model.  The spatially distributed rainfall–runoff model used in this study is based on the TOPMODEL concepts of Beven and Kirkby (1979), and simulates runoff generation by both the infiltration excess and saturation excess mechanisms. Simulations with the model revealed the highly complex nature of catchment response to rainfall events. Runoff generation was highly heterogeneous in both space and time, with the runoff response being governed by the spatial variability of soil properties and topography, and by the temporal variation in rainfall intensity. Although the model proved capable of simulating catchment response for many events, the investigation has demonstrated that not all aspects of the variability associated with agricultural catchments (particularly the effects of land management) can be captured using this relatively simple model. © 1997 by John Wiley & Sons, Ltd

Modelling runoff generation on small agricultural catchments: Can real world runoff responses be captured?

This paper addresses the question of similarity of runoff generation processes between catchments in the eastern wheat belt of Western Australia, and the use of dimensionless parameterizations to quantify this similarity. A spatially distributed rainfall-runoff model, simulating runoff generation by both the infiltration excess (Horton type) and saturation excess (Dunne type) mechanisms, was developed for catchments in the region. Seven small experimental catchments, with field-measured soil hydraulic properties and topography, were used in the study. Following on from the similarity theory developed by Sivapalan et al. (1987), a number of dimensionless similarity parameters were constructed using the field-measured soil and topographic properties, a characteristic length scale, and a characteristic flow velocity. The objective was to determine whether the dominant runoff generation mechanism on a catchment could be reliably predicted by these similarity parameters. This was achieved through sensitivity analyses carried out with the rainfall-runoff model. Two dimensionless parameters, K0* and ƒ*, were found to be critical for characterizing the similarity or dissimilarity of the runoff generation responses between the seven experimental catchments. Within the assumptions of the analysis, two catchments in the wheat belt region can be considered to be hydrologically similar, in terms of their runoff responses, if K0* and ƒ* are identical in both catchments. The dominant mechanism of runoff generation on any catchment can be reliably predicted, provided that the values of K0* and ƒ* are known. A partial quantification of the Dunne diagram (Dunne, 1978) for the wheat belt region, in terms of the infiltration excess and saturation excess mechanisms, was achieved by artificially varying K0* and ƒ* in the rainfall-runoff model to explore the full range of possible runoff generation responses.

Similarity analysis of runoff generation processes in real-world catchments

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Modelling runoff generation on small agricultural catchments: Can real world runoff responses be captured?

Similarity analysis of runoff generation processes in real-world catchments